Many Pagans have a problem with the word "sacrifice". I think this is because of its unfortunate association with the words "human" or "animal", or because it is sometimes associated with bargaining with the Gods. However, sacrifice was an important part of many ancient Pagan religions; to simply ignore it because we are uncomfortable with their implementation means that we may miss something worthwhile. The ancients sacrificed objects, money, animals, and sometimes, humans. We can easily restrict our sacrifices to a subset of these which are acceptable to modern ethics and sensibilities. Looking to the past for religious inspiration in no way requires that we bring forward practices which would now be considered barbaric.
In a modern context, sacrifice is the voluntary destruction or release of something dear. A sacrifice should be difficult to make and possibly uncomfortable to perform. It is important to differentiate making a sacrifice from making an offering, as offerings are functionally equivalent to small gifts (material or not) given to family or friends as a way of showing affection and maintaining a relationship. As such, the "gift of time" is an offering, not a sacrifice, for it is not a sacrifice to visit one's friends; rather, it's something that is done on a regular basis to keep the relationship in good working order, and to let them know you appreciate them. I would also distinguish sacrifice from communion, which is an offering that is shared between the celebrants and the Kindreds.
Sacrifice is different things to different people. To some, it may be the release of some sentimentally precious item; to others, it may be the creation and destruction of some work. Regardless, sacrificing an object renders it useless to you -- one cannot sacrifice an object for which one can easily find a replacement.
Why sacrifice? Different people will, naturally, have different reasons. My first sacrifice was an experiment. In general, I add a new practice to my religion after comparing it to a three-pronged standard: Is it historical? Does it work for modern times? Does it match my personal experience and belief? Typically, things that get answers of "yes" for at least two of those questions are temporarily added, with them being discarded again later if, after a reasonable period of time, I still cannot answer the "personal belief" question with the affirmative. I tried sacrifice for the first time because it was historical and could be adapted to work in modern times without doing violence to the theology behind it. Experience convinced me to keep the practice.
My experience with sacrifice has led me to believe that, like many things, it is best understood when compared to relationships with family. While there is a trade in sacrifice, it's not equivalent to the trade that happens when one purchases something from a store. Rather, it is like the trading that happens in normal, healthy relationships. When I give my husband a massage, I don't do this because he just did something nice for me -- I do it because I love him and because I know that he enjoys it. On the other hand, if he stopped showing me his appreciation with similar niceties (barring extreme circumstances, such as illness), I would eventually stop as well, and our relationship would probably falter.
Relationships sometimes require larger sacrifices too, although they happen less frequently. Sacrificing something for someone you love isn't done because you "owe" them something, nor is it done with the expectation of a specific return. It's done because it's sometimes necessary, and because that's the way relationships work. But neither are they one-sided; I assume that when I am willing to sacrifice something for a loved one, that they are willing to do the same for me.
Similarly, I give offerings and sacrifices to the Gods, not because I believe that I owe them or expect that they'll reward me in some way for doing so, but because these are mainstays of a relationship. To not ever give these things means that I'm expecting a very one-sided relationship. While relationships are sometimes uneven - parents, for example, can probably never be given as much as they give their children - there still needs to be an attempt at reciprocity.
Being in a relationship where one is willing to sacrifice something for the other is a different, more serious relationship than one where the participants are unwilling to sacrifice much. It moves the relationship into a different realm, to cross that threshold where you're willing to do more and more for the other. As such, it is a scary threshold, especially the first time it's crossed.
That threshold is a difficult one in any relationship. My first religious sacrifice was a poem. I composed it, read it aloud during my ritual, and then burned it. I have no other copies, and I made an effort not to memorize any portions of it. Right before I struck the match, I had a moment of serious doubt -- here I was, about to destroy a creative work of mine, and if all I believed was wrong, I'd have done it for nothing. I had a lot of other worries, too - after all, I had asked Brighid for inspiration to write this very poem which was, in turn, being sacrificed to Her. And, I worried that I hadn't poured as much of myself into it as I should have, as I knew when I wrote it what its purpose would be.
In the end, it was the actual burning that caused the most fear. I think that's the difference between a sacrifice and an offering. There's a profound act of faith in sacrificing something - the faith that you're not just standing in an empty room destroying something for no reason. I suspect that this threshold - the moment of fear - will never go away. Regardless of the result of whatever previous sacrifice I've offered, I think I'll have difficulty doing it again in the actual moment. I think, perhaps, that that's the point of it all.
Sacrificing is another method for mystical connection between the Divine and human; one that is perhaps particularly compelling because of its parallels to human relationships. That it has fallen out of disuse does not mean that there is something intrinsically wrong with it. It merely means that understanding it requires a bit more work than other, perhaps better understood methods.